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GEOMETRY: Chapter 10 10.1: Tangents to Circles

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A circle is the set of all points in a plane that are equidistant from a given point called the center of the circle. A circle with center P can be written P. A segment whose endpoints are the center of any point on the circle is a radius. A chord is a segment whose endpoints are on a circle. A diameter is a chord that contains the center of a circle. Image taken from:http://www.pecoglassbending.com/images/Circle%20terms.jpg

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A secant is a line that intersects a circle in two points. A tangent is a line in the plane of a circle that intersects the circle in exactly one point, the point of tangency. The tangent ray and the tangent segment are also called tangents. Image taken from: http://literacy.calumet.purdue.edu/STUDENT/bakerl3/secant_tangent.gif

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Ex.1: Tell whether the line or segment is best described as a radius, chord, diameter, secant, or tangent of circle C. Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 652.

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Ex.1: Tell whether the line or segment is best described as a radius, chord, diameter, secant, or tangent of circle C. Answer: a) radius; b) secant; c) diameter; d) tangent Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 652.

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Ex.2: Use the diagram to find the given lengths. a.Radius of circle B b.Diameter of circle A c.Radius of circle A d.Diameter of circle B Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 653.

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Ex.2: Use the diagram to find the given lengths. a.Radius of circle B b.Diameter of circle A c.Radius of circle A d.Diameter of circle B Answer: a) 3 units; b) 4 units; c) 2 units; d) 6 units Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 653.

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COPLANAR CIRCLES—Two circles can intersect in two points, one point, or two points. Coplanar circles that intersect in one point are called tangent circles. Coplanar circles that have a common center are called concentric. Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 652.

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Common Tangents—A line, ray, or segment that is tangent to two coplanar circles is called a common tangent. Image taken from: http://mtl.math.uiuc.edu/modules/dynamic/lessons/les4_7.gif

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Ex.3: Tell how many common tangents the circles have and draw them. Answer: a. 2 common tangents; b. 4 common; c. 3 common tangents Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 653.

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Ex.3: Tell how many common tangents the circles have and draw them. Answer: a. 2 common tangents; b. 4 common; c. 3 common tangents Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 653.

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Theorem 10.1and 10.2: Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 653. In a plane, a line is tangent to a circle if and only if the line is perpendicular to a radius of the circle at its endpoint on the circle.

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Ex.4: Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 653.

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Ex.4: Answer:No. 25 2 + 60 2 =4225, but 67 2 =4489 Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 653.

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Ex.5: Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 654.

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Ex.5: Answer: 14 cm Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 654.

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Theorem 10.3: Image taken from:http://www.partnership.mmu.ac.uk/cme/Geometry/CircleGeom/Images/Tangent.jpg Tangent Segments from a common external point are congruent.

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Ex.6: Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 654.

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Ex.6: Answer: 5.5 Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 654.

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10.1, p. 599, #6-29 all

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